Transcript ppt

Phys 102 – Lecture 16
Electromagnetic wave energy & polarization
1
Today we will...
• Learn about properties of electromagnetic waves
Energy density & intensity
Polarization – linear, circular, unpolarized
• Apply those concepts
Linear polarizers
Optical activity
Circular dichroism
Phys. 102, Lecture 16, Slide 2
E & B field energy density
There is energy stored in an E & B field
B
A
Parallel plate
capacitor
d
E
Solenoid
Recall Lect. 6
1
1 ε0 A
1
2
2
U C  CV 
 Ed   ε0 E 2 Ad
2
2 d
2
Volume containing
E field
It is convenient to define energy density = energy per volume [J/m3]
1
u E  ε0 E 2
2
These expressions are correct
for any E & B field in a vacuum
1 2
uB 
B
2 μ0
Phys. 102, Lecture 16, Slide 3
EM wave energy
There is energy stored in an EM wave in oscillating E & B fields
E0
B(t)
B0
E(t)
Since E and B oscillate, we measure the average energy density
uE
1
1
2
2
 ε0 E  ε0 Erms
2
2
Erms 
1
1 2
B2 
Brms
2 μ0
2 μ0
Brms 
uB 
utot
1
E0
2
1
B0
2
2
B
1
1
2
2
2
 ε0 Erms
 rms
 ε0 Erms

Brms
μ0
2
2 μ0
E & B field amplitudes
Recall that
E (t )  cB(t )
c 1
ε0 μ0
Phys. 102, Lecture 16, Slide 4
EM wave intensity
A source of light emits EM energy
at a rate given by the power P:
P 
 U
Units: W
t
Same energy flows through surfaces at larger distances, but
spread over a larger surface area A.
Energy flowing through surface in time Δt:
 U  utot Act
It is useful to define intensity:
I S
P
A
 utot c
Units: W/m2
Intensity corresponds to “brightness” of light
Phys. 102, Lecture 16, Slide 5
ACT: EM wave intensity
IP is the light intensity at a point P a distance r from a point
source, a 60 W light bulb. (Assume all electric power goes into EM wave)
r
IP
?
2r
What is the light intensity at a distance 2r?
A. 2IP
B. IP
C. IP/2
D. IP/4
Phys. 102, Lecture 16, Slide 6
Calculation: EM power
A light bulb emits an average 60 W of power. Calculate Erms & Brms
at a distance r = 2 m from bulb. (Assume all electric power goes into EM wave)
r=2m
By energy conservation, power emitted =
power through spherical surface at r = 2 m
P  IA  utot c 4πr 2
2
utot  ε0 Erms
Phys. 102, Lecture 16, Slide 7
CheckPoint 1.1–1.7
Longitudinal waves: oscillations
are || to direction or propagation
λ
DEMO
Expanded air
λ
Ex: Light
Radio waves
X-rays
Microwaves
Water waves
“The wave”
Ex: Sound
Compressed air
Transverse waves: oscillations
are  to direction of propagation
All EM waves!
E
B
Phys. 102, Lecture 16, Slide 8
Polarization
EM waves are transverse and have polarization – by convention,
the direction of the E field oscillation
z
z
E
Linear
y
B
x
z
Circular
Ex: “Vertical” polarization
z
E
y
x
x
x
B
Ex: “Left” circular polarization
Unpolarized – direction is random
For convenience we will stop showing the B field
Phys. 102, Lecture 16, Slide 9
Linear polarizers
Linear polarizers consist of || metal lines that absorb || E field.
Transmission axis (TA) is defined in direction that E field passes
TA
E  TA: no light passes
E
TA
E
E || TA: light passes
What happens for other angles between polarization and TA?
Phys. 102, Lecture 16, Slide 10
Law of Malus
Given angle θ between TA and polarization of incident EM wave:
Einc θ
Einc
θ E
trans
TA
TA
Component of E field  to TA axis is absorbed:
Einc
Eabs TA
Etrans  Einc cos θ
Since I  utot c  E
θ
Etrans
Itrans
Iinc
2
Itrans  Iinc cos2 θ
Light emerges with polarization || to TA axis
0
180
θ
360
Phys. 102, Lecture 16, Slide 11
ACT: polarizer
A vertically polarized EM wave passes through a linear polarizer
with TA at 45°
Einc
TA
What is the direction of the B field after the polarizer?
A.
B.
C.
D.
What is the magnitude?
Phys. 102, Lecture 16, Slide 12
Calculation: unpolarized light
Unpolarized light is incident on a linear polarizer. What is the
transmitted intensity?
TA
Einc
Etrans
Unpolarized light has an equal mixture of all possible θ’s
Itrans
Itrans  Iinc cos2 θ average over all θ:
Iinc
Iinc/2
0
180
I trans
θ
1
 I inc
2
360
Light emerges with polarization || to TA axis
Phys. 102, Lecture 16, Slide 13
ACT: CheckPoint 2.1
Unpolarized light passes through a linear polarizer with a
vertical TA.
I0
TA
What is the intensity of light when it emerges?
A. zero
B. 1/2 what it was before
C. 1/4 what it was before
D. 1/3 what it was before
Phys. 102, Lecture 16, Slide 14
ACT: CheckPoint 2.2
Now the light that emerged from the previous polarizer passes
through a second linear polarizer with a horizontal TA.
1
2
I0
TA
TA
What is the intensity of light when it emerges?
A. zero
B. 1/2 what it was before
C. 1/4 what it was before
D. 1/3 what it was before
Phys. 102, Lecture 16, Slide 15
ACT: 3 polarizers
Now suppose we add a third polarizer between the two outer
polarizers. The polarizer TA is tilted from vertical.
1
3
I0
2
TA
TA
TA
What is the intensity of the light that emerges?
A. zero, same as before
B. more than what it was before
C. need more information
DEMO
Phys. 102, Lecture 16, Slide 16
Calculation: 3 polarizers
1
3
I0
2
TA
TA
TA
Phys. 102, Lecture 16, Slide 17
Chirality & optical activity
Many organic molecules are chiral – they have “handedness”
L-alanine
D-alanine (unnatural
enantiometer)
Chiral molecules rotate linearly polarized light – optical activity
DEMO
“Dextrorotary” CW rotation
“Levorotary” CCW rotation
Phys. 102, Lecture 16, Slide 18
Circular dichroism
Chiral molecules also absorb left vs. right circularly polarized
light differently
Circular dichroism (CD) measures difference in absorption
Tool to distinguish chiral features in biomolecules
CD spectra
α-helix (right-handed helix)
Phys. 102, Lecture 16, Slide 19
ACT: Law of Malus
A
θ01 = 60°
I0
1
TA
B
θ01 = 60°
I0
1
2
2
TA
TA
TA
Compare the light emerging from the two polarizers in A and B:
A. I2A > I2B
B. I2A = I2B
C. I2A < I2B
Phys. 102, Lecture 16, Slide 20
Summary of today’s lecture
• Electromagnetic waves
Carry energy in E and B fields – energy density & intensity
Are transverse & polarized – linear, circular, unpolarized
• Applications
Linear polarizers – Law of Malus
Optical activity
Circular dichroism
Phys. 102, Lecture 16, Slide 21